Infinite Strip

in mathematics, the set of points in a plane that lie between two parallel lines in the plane. The x and y coordinates of the points in the strip satisfy the inequalities C₁ < Ax + By < C₂, where A, B, C₁, and C₂ are constants, with A and B not both zero. The transformation w = e^z conformally maps the strip 0 < y < π in the complex plane z = x + iy onto the upper half of the complex w-plane.